Infram publication no.

Geometrical design of coastal structures

Jentsje W. van der Meer

Published as Chapter 9 in “Dikes and revetments. Design, maintenance and

safety assessment”. Editor Krystian W. Pilarczyk, Balkema, Rotterdam

September 1998 CHAPTER 9

Geometrical design of coastal structures

Jentsje W. van der Meer

Consultants for Infrastructure appraisal and management, Infram

1 INTRODUCTION

The main contours of a coastal structure are determined by the choice of the type of structureand by the functional requirements. These functional requirements determine, for instance, thelayout of the structure and also the required crest height. During the conceptual design phaseand later on during the final design, the geometry of the structure will be established. Thisincludes the shape of the structure with the various materials used with their dimensions andlayer thickness. This chapter deals first with the functional design of coastal structures and the varioustypes that exist. The geometrical design of seawalls/dikes and of breakwaters is then treatedseparately and more in depth. Various design aspects are treated in other chapters. Wave run-up and wave overtopping has been described in chapter 8 and the formulae given there can beused to determine the crest height of dikes and seawalls. Filter structures and design ofarmour layers are treated in chapters 10 and 11, respectively. Other types of protection of theseaward side of seawalls and dikes are described in chapters 12-18. References for geometrical, functional and conceptual design are CUR/RWS (1995),CIRIA/CUR (1991), Pilarczyk, ed. (1990) and van der Meer (1993).

2 FUNCTIONAL DESIGN

Design of coastal structures should be based upon the functional requirements taking intoaccount the environmental conditions in the project area and giving due regard toconstructional aspects, operation and maintenance. The function of a flood protecting coastalstructure is mainly to protect the hinterland against the adverse effect of high water andwaves. If high water protection is required the structure should have a height well above themaximum level of wave run-up during storm surges. This normally calls for high crestelevations. If, however, some overtopping is allowed in view of the character of the hinterland, thedesign requirement is formulated in terms of the allowable amount of overtopping. Averageovertopping discharge values of 1-10 liters per second per running meter of dike may beaccepted for instance. Obviously crest elevations can be reduced considerably in this case. For structures, such as breakwaters, where wave reduction is the main objective, a furtherreduction in crest height can be applied. Wave heights due to transmission and overtoppingshould be negligible during operational conditions, but may reach values of the transmittedwave height of 0.3 m to 1 m in extreme design conditions.

1 Finally, training walls are mainly used to direct flow. The crest elevation is mainlydetermined by constructional aspects which implies that a minimum level of 2 m above meanhigh water should be applied to guarantee an uninterrupted progress of work (van der Weide,1989). Wave overtopping during operational and extreme conditions is of less concern in thiscase.

3 TYPES OF STRUCTURES

3.1 General

Generation of design concepts is based on both the functional requirements and theexperience and creative thinking of the designer (CUR/RWS, 1995). An important criterion inselecting alternatives for further development into well-defined structural concepts is thefailure risk involved in the various alternatives, and the relation of this risk to theircorresponding benefits. CUR/RWS (1995) gives the following categories of structures whererock is the basic material: • seawalls and dikes • breakwaters • groynes and shore protection breakwaters • gravel beaches • offshore bed or scour protection • closure dams • barriers, weirs and sills • bank protection • river training works, including spur dikes • bridge priers and abutments • spillways and outletsOnly the first two categories, seawalls/dikes and breakwaters will be treated in this chapter.

3.2 Seawalls and dikes

Common characteristics for all coastal and shoreline defence structures are in close relation tothe land, both in relation to functions and for construction. Seawalls and dikes usually borderon shallow water with the corresponding hydraulic loadings. Seawalls have been constructed with a wide variety of materials and cross-sections. Themost common types of seawall cross-sections are shown in Figure 1 (CUR/RWS, 1995).These are: • slope protection (with or without berm) • reclamation bund • rehabilitation mound of an existing vertical wall • anti-scour mat in front of an existing vertical wall

Dikes usually have a rather mild slope, mostly of the order of 1:2 or milder. A dike consists of atoe construction, an outer slope, often with a berm, a crest of a certain height and an inner slope,see Figure 1 of chapter 8. Figure 2 shows a schematisation of a dike on a distorted scale. Theouter slope may consist of various materials such as asphalt, a revetment of concrete blocks, orgrass on a clay cover layer. Combinations of these are also possible. Slopes are not alwaysstraight; the upper and lower parts do not always have a similar gradient if a berm has beenapplied. Figure 3 gives another example of the seaward side of a dike.

2 Figure 1 Basic seawall concepts (from CUR/CIRIA, 1995)

Figure 2 Schematisation of a dike (distorted scale)

Figure 3 Example of dike protection (from Pilarczyk, ed., 1990)

33.3 Breakwaters

Both the alignment and the cross-section of a breakwater affect -to a certain extent- thehydraulic loading of the armour or cover layer. Moreover, the bulk volume of a breakwater ismainly determined by these geometrical characteristics. In many cases breakwaters areexposed to relatively heavy wave loadings because of their protruding situation.

Given the strong dependency of the required armour strength on the wave height, oftenhigh demands must be made upon the armour elements, construction techniques andequipment. Depending upon the specific function to the breakwater, overtopping may beallowed or not, a choice which has important consequences for the design of the structure.The most common breakwater concepts are shown in Figure 4 and given by CUR/CIRIA(1995): • conventional rubble mound breakwater • berm breakwater • reef type structure • low-crested/submerged breakwater • caisson breakwater on rock foundation • composite caisson/rubble mound breakwater

Figure 4 Basic breakwater concepts (from CUR/CIRIA, 1995)

4 GEOMETRICAL DESIGN OF DIKES AND SEAWALLS

4.1 Loading zones

The degree of wave attack on a dike or seawall during a storm surge depends on theorientation in relation to the direction of the storm, the duration and strength of the wind, theextend of the water surface fronting the seawall and the bottom topography of the areainvolved. For coastal areas there is mostly a certain correlation between the water level (tideplus wind set-up) and the height of the waves, because wind set-up and waves are both caused 4by wind. Therefore, the joined frequency distribution of water levels and waves seems to bethe most appropriate for the design purposes (Pilarczyk, ed., 1990). For seawalls and dikes in the tidal region, fronting deep water, the following approximatezones can be distinguished: • the zone permanently submerged. This zone is not present in the case of a high level foreshore • the zone between MLW and MHW; the ever-present wave loading of low intensity is of importance for the long-term behaviour of the structure • the zone between MHW and the design level; this zone can be heavily attacked by waves, but the frequency of such attack reduces as one goes higher up the slope • the zone above design level, where there should only be wave run-up.

A bank slope revetment in principle functions no differently under normal circumstances

than under extreme conditions. The accent is, however, more on the persistent character of thewave attack rather than on its size. The quality of the seaward slope can, prior to theoccurrence of the extreme situation, already be damaged during relatively normal conditionsto such a degree that its strength is no longer sufficient to provide protection during theextreme storm. The division of the slope into loading zones has not only direct connection with the safetyagainst failure of the revetment and the dike as a whole, but also with different application ofmaterials and execution and maintenance methods for each zone, see for instances Figure 3. Itis emphasized that for each design phase these alternatives should be elaborated at acomparable level of detail. The same applies to the construction alternatives which may havea great influence on the total structure cost.

4.2 Dike or seawall shape

The average slope angle of the bank may not be so steep that the whole slope or revetmentcan loose stability through sliding. This criterion gives the maximum slope angle. Gentler (flatter) slopes lead to a reduced wave force on the revetment and less wave run-up; wave energy is dissipated over a greater length. By using the wave run-up or waveovertopping approach (chapter 8) for calculations of the crest height of a trapezoidal profile ofa dike for different slope angles, the minimum volume of the embankment can be obtained. However, this does not necessarily imply that minimum earth volume coincides withminimum costs. An expensive part of the embankment comprises the revetment of theseaward side slope and the slope surface increases as the slope angle decreases. The optimumcross-section, based on costs, can be determined if the costs of earth works per m3 and thoseof the revetment per m2 are known. Careful attention is needed, however, because therevetment costs are not always independent of the slope angle. For example, for steep slopesheavy protection is required while for mild slopes the cheaper grass mat can often provide asufficient protection. Another point of economic optimization can be the available space for dike constructionor improvement. Common Dutch practice for a dike is to apply a slope of 1:3 on the inner slope andbetween 1:3 and 1:5 on the seaward slope. The minimum crest width is 2 m. The seaward sideberm is a common element in Dutch dike construction. It could in the past lead to a reductionin the expenditure on stone revetments as on a very gentle sloping berm a good grass mat canbe maintained and it produced an appreciable reduction in wave run-up.

5 Present practice, in order to obtain a substantial reduction in wave run-up or waveovertopping, is to place the outer berm at or close to the water level of the design storm flood.If the berm lies too much below that level the highest storm flood waves would not breakbeneath or on the berm and the run-up will be inadequately affected, the grass mat on theupper slope too heavily loaded by waves which may lead to possible erosion. For the stormflood berm at the high design levels as in the Netherlands (design return period 10,000 years)there are in general no problems with the growth of grass on the berm and the upper slope. However, there can be circumstances which require also the application of a hardrevetment on the berm and even on a part of the upper slope. This is the case when high waterlevels frequently occur, leading to more frequent run-up on the upper part by salt water. Acommon grass mat can only survive a few salty events a year. An important function of the berm can be its use as an access road for dike maintenance.In general care should be taken to prevent erosion of the grass mat at the junction with therevetment. The abrupt change in roughness may lead to more local erosion. It is advised tocreate a transition zone by applying cell-blocks, geogrids or other systems allowingvegetation. The influence of slope angle and the application of a berm is shown in Figure 5. Threecross-sections have been drawn, all with the same wave run-up level. The steepest slope 1:3gives the highest crest height. A gentler slope 1:4 reduces the crest height and even thevolume required for the dike. A berm gives another reduction in dike height and volume.

Figure 5 Example of different dike shapes and height with the same 2%-wave run-up level (from Pilarczyk, ed., 1990)

4.3 Dike or seawall height

The height of a dike for many centuries has been based on the highest known flood level thatcould be remembered. It is evident that in this way the real risk of damage or the probabilityof flooding was unknown. Little was known about the relation between the cost to preventflooding and the cost of damage that might result from flooding. In the twentieth century it was found that the occurrence of extremely high water levelsand wave heights could adequately be described by probability distributions. However, theextreme distributions, often based on relatively short periods of observations, mostly have tobe extrapolated into regions far beyond the field of observations.

6 After the 1953 disaster the probability of flooding was studied in the Netherlands inrelation to the economical aspects. Finally, it was decided to base the design of most of thesea dikes on a storm surge level with a return period of 10,000 years. The main reason for thislarge return period is the enormous economical damage that occurs if dikes in the low layingareas of Holland breach. It is much cheaper to build higher dikes than to bear the costs of aflooding. This may be different in other areas, for example in the UK, where only small areas willbe affected and where the inundation depth may be smaller than in the Netherlands. In the Netherlands the wind set-up is mostly incorporated in the estimated storm surgelevel. If it is not the case, the wind set-up should be calculated separately and added to thedesign water level. Besides the design flood level various other elements play a role indetermining the design crest level, see Figure 6:

Figure 6 Important aspects when computing the dike height

• wave run-up or overtopping height. Depends on wave height and period, wave angle of approach, roughness and permeability of the slope, and the profile shape. See chapter 8. • an extra margin to the dike height to take into account seiches (oscillations) and gust bumps (single waves resulting form a sudden violent rush of wind); this margin in the Netherlands varies from 0-0.3 m for the seiches and 0-0.5 m for the gust bumps, depending on the location. • a change in bottom level or a rise of the mean sea level (the forecast for the estimated life time of the structure). • settlement of the subsoil and the dike body during its life time.

The combination of all these factors mentioned above defines the crest freeboard of the dikeand the dike height for construction.

5 GEOMETRICAL DESIGN OF BREAKWATERS

5.1 Crest height

Wave run-upThe crest height of seawalls with rubble mound protection or armouring may well bedetermined by an allowable overtopping percentage. This means that under design conditionsonly a few percentage of the waves may reach the crest and inner side of the structure. Aformula for the 2%-wave run-up has been given in chapter 8. Figure 7 gives the formula in agraph and gives a comparison with a smooth slope. In many situations a rock structure canhave a much lower crest height than a smooth structure like a dike.

7 Figure 7 Wave run-up (2%) on rock slopes

It is also possible to allow a larger overtopping percentage under design conditions, but forpercentages larger than about 10-15 the overtopping waves will generate a transmitted waveheight behind the structure which may become about 10% of the incident wave height. Vander Meer (1993) gives a formula for the distribution of the run-up levels on a rock slope.Based on that formula it is possible to determine the crest height of a rock structure for anydesired overtopping percentage.

Simple formula for wave transmission

In most cases the crest height is determined by a limited allowable wave height behind thestructure, the so-called transmitted wave height. The transmission coefficient Ct is the ratio oftransmitted and incident wave height. An overall view of available data on wave transmissionis given in Figure 8 (van der Meer, 1993). The most simple relationship can be found if thetransmission coefficient is related to the relative crest freeboard, i.e. the difference betweenthe design water level (see Figure 6) and the crest freeboard Rc/Hi. A value of 1 means thatthe crest height is one wave height above the water level, a value of 0 gives a structure withthe crest level at the water level.

The fitted relationships in Figure 8 may be described as follows:

for -2 < Rc/Hi < -1.13 Ct = 0.8

The relationships give a simplistic description of the data available, but will often besufficient for preliminary design. The upper and lower bounds of the data considered aregiven by the 90% confidence bands. The standard deviation, measured vertically, isσCt = 0.09.

Sophisticated approach on wave transmission

More recent research by de Jong (1996) and d’Angremond et al. (1996) has given theinfluence of wave steepness, slope angle and the crest width on wave transmission. Theprinciple equation is similar to formula 1, i.e. a straight decreasing line from large to smallwave transmission with Rc/Hi as parameter (see Figure 8):

Ct = a – 0.4 Rc/Hi with a maximum of Ct = 0.8 and a minimum of Ct = 0.075 (2)

The parameter “a” describes all the other relevant influences:

a = (B/Hi)-0.31 * (1 – e-0.5ξ) * Astr (3)

with: B = crest width

ξ = breaker parameter, see formula 1 in chapter 8 Astr = a coefficient depending on the type of structure:

rock slopes and concrete units: Astr = 0.64

The standard deviation around formula (2) is given by σCt = 0.06, resulting in a 90%confidence band of Ct ± 0.10, a considerable improvement with respect to formula 1.

9Percentage of overtopping waves related to wave transmission Not all incident waves will overtop a low-crested structure. The lower the crest of thestructure the more waves will overtop and increase wave transmission. Project-related scalemodel tests at Delft Hydraulics have given the relationship between the percentage ofovertopping waves and the wave transmission. The tests were related to conventionalbreakwater cross-sections, armoured with tetrapods or accropode and the crest had a (low)concrete superstructure. Overtopping was defined as wave passing the front wall of the superstructure and this wasmeasured with a wave gauge. An overtopping wave hit the gauge and gave a peak on thesignal. All the peaks (overtopping waves) were counted and related to the total of incidentwaves. This gave the overtopping percentage. Figure 9 gives the percentage of overtopping waves as a function of the relative crestfreeboard. It appeared that the armour size had influence on the percentage of overtoppingwaves. The relative crest freeboard, therefore, was defined by Rc*Dn/Hi2. The nominaldiameter Dn is the cubical size of a unit and is described in chapter 11. The figure gives nodifference between tetrapods and accropode. Figure 10 gives the corresponding wave transmission coefficients in a similar way as inFigure 8. Wave transmission was not measured in all the tests given in Figure 9. Figure 10shows that for high crests, say Rc/Hi > 1, always some wave transmission can be expected.This wave transmission goes through the breakwater and is not generated by overtoppingwaves.

Figure 9 Percentage of overtopping waves as a function of

A breakwater consists of various parts as can be seen in Figure 11. The core and toe may bebased on filter layers which protect sand coming through the rock. In order to have a smoothtransition from core to bigger rock or artificial units one or more under layers may bedesigned. The armour layer may be continued over the crest (low-crested structures) or asuperstructure may be designed. A superstructure gives easy access to the breakwater. The design of armour layers has been given in chapter 11. Scouring and toe protectionshave been described in chapters 7 and 18 respectively.

Figure 11 Cross-section of a conventional breakwater

11 Some general points and design rules for the geometrical design of the cross-section willbe given here. These are: • the minimum crest width • the thickness of (armour) layers • the number of units or rocks per surface area • the grading of rock • the bottom elevation of the armour layer • the supporting toe • the crown wall

The crest width is often determined by construction methods used (access on the core bytrucks or crane) or by functional requirements (road/crown wall on the top). Where the widthof the crest can be small a required minimum width Bmin should be provided, where (SPM,1984):

Table 1 Values of kt and nv (SPM, 1984)

The number of units in a rock layer depends on the grading of the rock. The values of ktthat are given above describe a rather narrow grading (uniform rock). For riprap and evenwider graded material the number of rocks cannot easily be estimated. In that case the volumeof the rock on the structure can be used.

12 The grading of the rock can be given by D85/D15, where D85 and D15 are the 85% and 15%values of the sieve curves, or by Dn85/Dn15, based on the mass distribution curves. Examplesof gradings are shown in Table 2 showing the relationship between class of stone and D85/D15.Further details of recommended methods of specifying gradings and of suggested gradings aregiven in CUR/CIRIA (1991).

The bottom elevation of the armour should be extended down slope to an elevation belowminimum still-water level of at least one (significant) wave height, if the wave height is notlimited by the water depth. Under depth limited conditions the armour layer should beextended to the bottom as shown in Figure 11 and supported by a toe.

5.3 Supporting toe

In most cases the armour layer on the seaside near the bottom is protected by a supporting toe,see Figure 11. If the rock in the toe has the same dimensions as the armour, the toe will bestable. In most cases, however, one wants to reduce the rock size in the toe. The most simplerelationship is assumed if the stability number Hs/∆Dn50 (see chapter 11) is related to therelative depth ht/h, where ht is the depth of the toe below still-water level and h is the waterdepth just in front of the toe. CIRIA/CUR (1991) and van der Meer (1993) gave thisrelationship with a small number of tests from Delft Hydraulics (DH) and the DanishHydraulic Institute (DHI). Later Gerding (1993) conducted small scale model tests speciallyon toe stability, see also van der Meer et al. (1995). First of all the damage level was better defined. The damage level Nod was used (see alsochapter 11). This is the actual number of displaced stones related to a width, along thelongitudinal axis of the structure, of one nominal diameter Dn50. Nod = 0.5 means start ofdamage (a safe figure for design), Nod = 2 gives some flattening out and Nod = 4 meanscomplete flattening out of the toe. This applies to a “standard” toe size of about 3 – 5 stoneswide and 2 – 3 stones high. For wider toe structures a higher damage level can be appliedbefore flattening out occurs. One of the conclusions of the research was that wave steepness had no influence onstability. Van der Meer et al. (1995) gave an improved formula with respect to toe stability,where the toe depth was given as ht/Dn50. As Dn50 appeared also in the stability numberHs/∆Dn50 it was found later on that for low toe structures unrealistic (even negative!) requiredtoe diameters could be calculated. Therefore, Gerding’s work has been re-analysed. Figure 12gives all his data with a design formula. This formula is almost similar to the original simple

13formula of van der Meer (1993), but based on more data points. The formula on toe stabilitycan be written as follows:

Hs/∆Dn50 * Nod-0.15 = 2 + 6.2 (ht/h)2.7 (7)

A high toe, say ht/h < 0.4 comes close to a berm and, therefore, close to the stability of thearmour layer. Armour layers have stability numbers close to Hs/∆Dn50 = 2. This is the reasonthat formula 7 does not start in the origin, but at Hs/∆Dn50 * Nod-0.15 = 2 for ht/h = 0. Formula 7can be used in the range:

0.4 < ht/h < 0.9

5.4 Crown walls

For a number of reasons the introduction of a crown wall on top of a breakwater can beconsidered (CUR/RWS, 1995): • rubble mound breakwaters are often designed to sustain some damage and access across the breakwater is needed for repairs • a crown wall with parapet may lead to a substantial reduction in the amount of stone which would otherwise be needed for a comparable conventional design (see Figure 11) • with overtopping the crown wall may limit the width of the mound and by its shape protect the lee side slope.

There are also certain disadvantages related to a crown wall which should be taken intoaccount in selection and design: • the crown wall represents a rigid element in a structure which is flexible by nature. Uneven settlements may lead to great problems for the elements of the crown wall and even more to transport facilities

14 • increase of the parapet wall, in order to reduce the volume of stones, leads to very large wave impact forces on this wall. Such a design should be avoided. • overtopping water becomes concentrated more into a jet and is a potential danger for the lee side armour

The design of crown walls should commence with an assessment of their stability.CUR/RWS, 1995, gives some basic rules and more detailed information can be found inPedersen, 1996. In summary, apart from the weight of the crown wall, wave forces form theonly other significant load. Other practical details can be found in CUR/RWS, 1995.